It was an interesting tradition or belief that the King's touch was able to cure scrofula, which was a disease at the time. Note how this passage is set in a scene that very much compares and constrasts the King of England with Macbeth, who is now the King of Scotland. Of course, the goodness and the way that the King of England is divinely appointed to his role is emphasised, compared to Macbeth, who has seized the crown. The number of omens and supernatural events that occur obviously indicate that this was an unnatural event that has gone against nature.

However, the words of the doctor in the quote you have highlighted refer to the King of England and his goodness in using his divine power to cure the sick. He says that their sickness necessitates the greatest effort of medical skill, however the divine power that God has given him cures their illness at his touch.